1. Polynomial
s
What is
POLYNOMIAL?
An expression which is the sum of terms of the
form a x k where k is a nonnegative integer is a
polynomial.
Polynomials are usually written in standard
form.

2. Polynomial
s
Standard form means that the terms of the
polynomial are placed in descending order,
from largest degree to smallest degree.
Polynomial in standard form:
Degree
2 x 3 + 5x 2 – 4 x + 7
Leading coefficient Constant term

3. Polynomial
s
The degree of each term of a polynomial is
the exponent of the variable.
The degree of a polynomial is the largest
degree of its terms. When a polynomial is
written in standard form, the coefficient of the
first term is the leading coefficient.

4. Polynomial
s
Kinds of Polynomials
(according to number of terms)
A polynomial with only one term is called a
monomial.
A polynomial with two terms is called a binomial.
A polynomial with three terms is called a
trinomial.

5. Adding Polynomials
Find the sum. Write the answer in standard format.
(5x 3 – x + 2 x 2 + 7) + (3x 2 + 7 – 4 x) + (4x 2 – 8 – x 3)
SOLUTION
Vertical format: Write each expression in standard form. Align like terms.
5x 3 + 2 x 2 – x + 7
3x 2 – 4 x + 7
+ – x + 4x –8
3 2
4x 3 + 9x 2 – 5x + 6

6. Adding Polynomials
Find the sum. Write the answer in standard format.
(2 x 2 + x – 5) + (x + x 2 + 6)
SOLUTION
Horizontal format: Add like terms.
(2 x 2 + x – 5) + (x + x 2 + 6) = (2 x 2 + x 2) + (x + x) + (–5 + 6)
= 3x 2 + 2 x + 1

7. Subtracting Polynomials
Find the difference.
(–2 x 3 + 5x 2 – x + 8) – (–2 x 2 + 3x – 4)
SOLUTION
Use a vertical format. To subtract, you add the opposite. This means you
multiply each term in the subtracted polynomial by –1 and add.
–2 x 3 + 5x 2 – x + 8 No change –2 x 3 + 5x 2 – x + 8
– –2 x 3 + 3x – 4 Add the opposite + 2 x3 – 3x + 4

8. Subtracting Polynomials
Find the difference.
(–2 x 3 + 5x 2 – x + 8) – (–2 x 2 + 3x – 4)
SOLUTION
Use a vertical format. To subtract, you add the opposite. This means you
multiply each term in the subtracted polynomial by –1 and add.
–2 x 3 + 5x 2 – x + 8 –2 x 3 + 5x 2 – x + 8
– –2 x 3 + 3x – 4 + 2 x3 – 3x + 4
5x 2 – 4x + 12

9. Subtracting Polynomials
Find the difference.
(3x 2 – 5x + 3) – (2 x 2 – x – 4)
SOLUTION
Use a horizontal format.
(3x 2 – 5x + 3) – (2 x 2 – x – 4) = (3x 2 – 5x + 3) + (–1)(2 x 2 – x – 4)
= (3x 2 – 5x + 3) – 2 x 2 + x + 4
= (3x 2 – 2 x 2) + (– 5x + x) + (3 + 4)
= x 2 – 4x + 7